Additional explanation

Thank you for making the reasoning very clear. I added another sentence to round up the argument. Please make sure that it's consistent and then flag accordingly.

Since my answers for the other questions were found to be lacking, I am verifying them using sage. So for this question:

A = Matrix(QQ, 4,5,[[1,2,1,3,2],[3,4,9,0,7],[2,3,5,1,8],[2,2,8,-3,5]])

v1 = vector(QQ,[1,3,2,2])

v2 = vector(QQ,[2,4,3,2])

v3 = vector(QQ,[3,0,1,-3])

span([v1,v2,v3],QQ) == A.column_space() // This evaluates as true, so done.